Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

A_1 Weights and d-Homogeneous Measures on Ahlfors d-Regular Space

Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.

Remark on Regularity of Continuous Operators on AL-Spaces

Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.

Some Properties of Regular and α-Regular (LM)-Spaces

In this paper, we give some properties of regular (LM)-spaces and α-regular (LM)-spaces and investigate the relationship among them.

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces

Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces

In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p < ∞, 1 ≤ q ≤ ∞, and analyticity of solutions with 1 < p < ∞, 1 ≤ q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.

LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

Near-Vector Spaces Constructed over Zp, for p a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

高斯感知约束空间异常的相关滤波目标跟踪

针对目标在复杂场景运动过程中容易出现跟踪丢失问题,提出一种高斯感知约束空间异常的目标跟踪算法。以高斯均匀分布为分布规律建立目标特征采样点,采用卷积结构提取目标的外观模型以及权重模型;为了约束空间异常,在目标函数中构建空间正则项,同时更新目标权重模型,减小空间过拟合的产生,增强跟踪器的空间异常适应性;应用加权最小二乘法思想,获得权重响应模型中心,确定目标中心,更新跟踪位置,增强跟踪器鲁棒性。使用OTB2015和UAV20L数据集,与其他主流相关滤波算法相比,该算法在目标运动导致低分辨率、遮挡等复杂条件下,跟踪成功率以及跟踪精度较高。

基于核机器的加速失效时间模型及其应用

加速失效时间模型是一种应用广泛的生存分析模型。本文借助LASSO惩罚剔除冗余预测变量,构建基于核机器的加速失效时间模型,用以刻画预测变量与生存期间的复杂关系。此外,提出一种新的正则化Garrotized核机器估计方法,可以较好地刻画预测变量与生存期潜在的非线性关系,实现非参数分量中预测变量间交互作用的自动建模,提升模型预测精度。模拟研究表明,与已有的代表性方法相比,本文提出的方法对生存期的预测精度更高,特别是在复杂关系情形下优势更为显著。最后,将该方法应用于胃癌数据分析,利用临床信息和基因表达预测生存期和风险评分。实证结果显示,该方法能为病例基于风险分层的临床精准诊疗方案设计提供有益的参考。

速度零耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性

该文研究速度零耗散,微旋转速度拉普拉斯耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性问题.通过构建两个组合量和使用Littlewood-Paley分解技术,该文建立了该系统解的全局正则性结果.

基于色度角信息的衡水湖富营养状态监测研究

【目的】营养状态作为评价湖库水环境变化特征的一个重要方面,实现对其准确、大范围的动态监测对于分析富营养化成因具有十分重要的作用。【方法】利用Landsat8遥感数据的色度角信息,构建了适用于衡水湖的叶绿素a浓度反演模型,并对其精度进行了检验,在此基础上,实现对衡水湖2013—2022年10 a间的营养状态监测,分析了其与气温和降水等气候因素的关系,对2018—2019年5次生态补水过程进行了遥感监测。【结果】结果表明:(1)该模型较为可靠,决定系数R^(2)为0.79,均方根误差和平均百分比误差分别为0.0018和4.5%;(2)近10 a衡水湖营养状态得到一定的改善,其空间变化呈现“北低南高”现象。其中,南关闸和南关新闸相对于其他湖体区域营养状态处于较高水平;(3)通过对5次生态补水过程的遥感监测发现,生态补水对于衡水湖营养状态改善具有一定的积极作用,尤其在进水口的王口闸附近,其对生态补水的响应最为及时。衡水湖营养状态是一个内在、外在、水动力等多因素影响的问题,对于个别区域存在些许波动,仍需进一步研究其内在关系。【结论】通过遥感手段实现对衡水湖营养状态的监测是可行的,能够较好揭示衡水湖营养状态变化整体规律,并实现对生态补水过程的有效监测,为衡水湖湿地水环境监测和营养状态治理提供重要的技术支撑。

Image decomposition using adaptive regularization and div(BMO)

In order to avoid staircasing effect and preserve small scale texture information for the classical total variation regularization, a new minimization energy functional model for image decomposition is proposed. Firstly, an adaptive regularization based on the local feature of images is introduced to substitute total variational regularization. The oscillatory component containing texture and/or noise is modeled in generalized function space div （BMO）. And then, the existence and uniqueness of the minimizer for proposed model are proved. Finally, the gradient descent flow of the Euler-Lagrange equations for the new model is numerically implemented by using a finite difference method. Experiments show that the proposed model is very robust to noise, and the staircasing effect is avoided efficiently, while edges and textures are well remained.

REGULARITY CRITERIA FOR WEAK SOLUTION TO THE 3D MAGNETOHYDRODYNAMIC EQUATIONS

In this article, regularity criteria for the 3D magnetohydrodynamic equations are investigated. Some sufficient integrability conditions on two components or the gradient of two components of u ＋ B and u - B in Morrey-Campanato spaces are obtained.

SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.

LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS

This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] （Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365： 806-808） and [18] （Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375：799 802）.

Combination and distribution of reservoir space in complex carbonate rocks

This paper discusses the reservoir space in carbonate rocks in terms of types,combination features,distribution regularity,and controlling factors,based on core observations and tests of the North Truva Oilfield,Caspian Basin.According to the reservoir space combinations,carbonate reservoirs can be divided into four types,i.e.,pore,fracture-pore,pore-cavity-fracture,and pore-cavity.Formation and distribution of these reservoirs is strongly controlled by deposition,diagenesis,and tectonism.In evaporated platform and restricted platform facies,the reservoirs are predominately affected by meteoric fresh water leaching in the supergene-para-syngenetic period and by uplifting and erosion in the late stage,making both platform facies contain all the above-mentioned four types of reservoirs,with various pores,such as dissolved cavities and dissolved fractures,or structural fractures occasionally in favorable structural locations.In open platform facies,the reservoirs deposited continuously in deeper water,in an environment of alternative high-energy shoals（where pore-fracture-type reservoirs are dominant） and low-energy shoals（where pore reservoirs are dominant）.

GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

The Theory of Vector-Valued Function in Locally Convex Space

In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.